I would like to do (1) an LPA of 21 continuous variables, and (2)test class membership in relations to 9 covariates (x's) and 2 distal outcomes (y's). I intend to use the procedure for manually implementing the 3-step approach described in M+ webnotes #15 v5.

In the 3-step approach, given that the measurement model is estimated independent of the auxiliary variables, does it make sense to proceed in the following manner?

1. Do class enumeration in Step 1 (e.g., do Step 1 with 1 - 8 classes) to identify the best one or two models while specifying AUXILIARY = x1, x2,..x9, y1, y2.

2. Do Step 2 (calculating measurement error for most likely class variable) for the best one or two models identified in class enumeration.

3. Do Step 3 (estimating the auxiliary model while specifying the latent class model with measurement errors obtained in Step 2) for the best one or two models from class enumeration.

Can latent class membership (C) be regressed on covariates?

Can distal outcomes be regressed on class membership in Step 3?

Is it accurate to say that class membership will not shift regardless of modifications in the auxiliary model (e.g., adding/removing covariates and distal outcomes)?

I tried it with vs. without the "CATEGORICAL = Y" statement. The regression results (p-values) for Y on X1-X3 are comparable in both cases. I see that I got an intercept for Y in each class when Y was modeled as continuous, as opposed to a threshold.

Could you please help me understand why I could not use "CATEGORICAL ARE" with binary distals?

What do I need to do to obtain P(distal=1), or odds of distal=1 in one class versus another class?

If I am doing the manual 3-step approach, I do not need to use the AUXILIARY= statement according to WebNote 15. (I only need to use AUXILIARY= in the automatic 3 step approach, e.g., using DU3STEP). Does that mean, in Step 3 of the manual 3-step approach, I can specify covariates and outcomes with CATEGORICAL= ?

Because when I used CATEGORICAL= at Step 3 of the manual 3-step approach with a binary outcome, I was able to get an output on "LOGISTIC REGRESSION ODDS RATIO RESULTS." I just want to verify that this is ok.

I am interested in testing whether means on a set of distal outcomes differ across growth trajectory classes (GMM), controlling for a set of covariates. The covariates have direct effects on growth factor means (class indicators) and the class indicators have direct effects on the outcomes within class (constrained equal across class). I used a one-step approach , but a reviewer suggested a 3-step approach. Two questions: (1) Can I test whether *adjusted* means for the distal outcomes differ between classes with a manual 3-step approach, and (2) Given the direct effects of covariates on class indicators (and class indicator effects on the distal outcomes) with entropy =.63 (obtained from the 1-step final model), would the 1-step approach be better suited than the 3-step approach based on simulation results in webnote 15. Thanks!

I don't think it is possible to do a 3-step approach for this model because you have a "class indicator effects on the distal outcomes". Since the class indicators are latent variables in stage 3 you cant use them (these latent variables, the growth factors, are measured and created in stage 1 only so they wont be available in stage 3).

I would like to use latent class membership from one series of indicators (along with a few other continuous covariates), to predict latent profile membership derived from a separate series of indicators. Clustering independently is theoretically important (separate domains), which is why the 3-step procedure is appealing.

I can manually run the 3-step procedure separately for each latent class analysis (at least up to the 2nd step), to get the misclassification stats for each one. A 4-profile/class solution fits best in both cases.

Something along the lines of Ex7.14 appears to be close to what I need, except that I have a directed prediction from theory (actually more similar to Ex7.19, with a separate clustering variable instead of the factor), and a number of continuous covariates.

So, what type of specification am I dealing with here, and how can I implement it (the auxiliary option doesn't seem designed to support this)?

I can imagine that an analysis with categorical misclassification might be probability-based/fuzzy, or might need some sort of MCMC sampling? As a fall back, entropy is high (>.90) in both cases, so I guess I could 'hard-code' most likely cluster membership and run something like a multinomial logistic regression with covariates?

We are using the manual 3-step method to test predictors in a latent transition analysis with three time-points. Changing the predictors changes our class sizes, particularly for the third time-point. Do you know why this is happening?

We have measurement non-invariance, so each LCA is estimated separately. The nominal most likely class variable is obtained from each LCA estimation, without constraining any of the item thresholds. Other than that, we are following the approach in Web Note 15 shown in Appendices L, M, N, and O.

You constrained the item thresholds in your individual LCAs so that they would be the same as the LCAs from the initial LTA, which had measurement invariance. You then used the most likely class variable from the individual LCAs to run a second LTA, this time with predictors. When you change your predictors, do the class sizes change?

This is the problem we are experiencing. We don't need to constrain item thresholds in our individual LCAs because they don't need to be the same as the LCAs from an initial LTA, because we don't want measurement invariance. The class sizes are changing considerably when we use the most likely class variable to run an LTA with predictors. We aren't changing the most likely class variable, we're just changing the predictors. Does that make sense?

I actually meant to refer to fixing the nominal parameters (not the threshold invariance) - I assume you are doing that fixing in the 3rd step. So you are following appendices H, I, J. Those don't have a covariate. You could do your analyses on the Appendix K generated data which include x and follow the H-I-J steps to see what happens. I don't think we have explored that.

You think we should generate data with measurement invariance and a covariate, estimate LCAs without assuming measurement invariance, and then test the influence of that same covariate on our class solutions? Wouldn't that illuminate the consequences of not assuming measurement invariance when it exists?

We would like to test the predictive strength of variables without changing the class solutions, like in r3step. It might be useful to generate data with two covariates and then test each independently to see if the class sizes change. However, we already have data and multiple covariates, and we already know the class sizes are changing. Why would this happen when we've fixed the probability of being in one class versus another?

I would like to use the 3-step approach to examine the effects of some covariates on latent trajectory classes. Because I have censored data, I cannot use the auxiliary function (R3STEP), as it does not run with algorithm = integration. I would like to use the manual 3-step approach but I do not know how to obtain the logits for the classification probabilities. In my output I only have the average latent class probabilities. How could I obtain classification probabilities or logits in growth mixture models?

I am running a model predicting continuous and categorical outcomes using a latent class variable and several covariates based on the manual 3 step procedure. I am freely estimating the means and thresholds of the Dvs for each class. I was wondering whether the means and thresholds of the DVs for each class are estimated values based on the mean value of all covariates in the model as a default or do I have to mean center them. We want to present the estimated means in a table for each class, but are unsure how they should be interpreted.

We are interested in using latent class as a predictor of a distal binary outcome (using the manual version of the 3-step approach). Specifically, in step 3 we want to test whether the thresholds for the binary outcome differ between our two classes. As far as we understand, we can do this with a Wald test using the Model Test statement -- that's what we did.

In our first model, we use only latent class as a predictor. We get the Wald test as requested, but we also get an odds ratio and its corresponding significance test, which is exactly what we want. In our second model, we use latent class and some covariates as predictors of the outcome. When we include the covariates, the odds ratio we are interested in is no longer provided, just the requested Wald test. Would it be accurate to compute an odds ratio ourselves using the covariate-adjusted thresholds from the output? Or if not, is there another way we can get this information from Mplus? We would like to be able to present the degree to which the odds ratio changes after taking into account the effects of the covariates on the outcome.

For both of your models you can express the odds ratio in Model Constraint using parameter labels from Model. That also gives you SEs so you can get a test. With covariates the odds ratio would be based on only the thresholds as you say.

From that, I have a follow-up question. I'm noticing that when I use Model Test to test threshold #2 = threshold #1 and compare that result to the "Latent Class Odds Ratio Results" that Mplus outputs automatically, or to the OR result from Model Constraint, I get quite different significance test results. The two OR significance tests are identical, but the test for the difference in thresholds from Model Test is quite different from the test of the OR. The only thought I've had is that the OR is being tested against a null value of 0 and not 1, but I'm not sure. I'm hoping someone can shed some light on my confusion.

Thanks. I have Mplus Version 7.2. My output does not have the table I asked about, logits. It does not have the table, "Classification Probabilities for the Most Likely Latent Class Membership (Row) by Latent Class (Column)". The output does have the table, "Average Latent Class Probabilities..."

The output is from nonparametric two-level mixture models that have categorical latent variables on both the within and between levels. These were demonstrated in Henry & Muthen, 2010, "Multilevel Latent Class Analysis: An Application...", Structural Equation Modeling, vol 17.

The output states that Auxiliary= is not available for R3STEP, DCON, etc., when there are latent variables on the between and within levels.

The desired model is: (1) use Time 1 indicators to derive latent classes, (2) regress a Time 2 distal outcome on Time 1 class membership, (3) use the Time 1 version of the Time 2 distal outcome as a latent class covariate/auxiliary.

Can this be done with the manual 3-step method if I have the table of logits (or table of classification probabilities to calculate the logits)? Thanks.